Chapter 10 (Unit 8): Quality Control

Learning Objective:

Learning Objectives:

1. List and briefly explain the elements in the control process

2. Explain how control charts are used to monitor a process, and the concepts that underlie their use

3. Use and interpret control charts

4. Perform run tests to check for nonrandomness in process output

5. Assess process capability

What is Quality Control?

1. A process that evaluates output relative to a standard and takes corrective action when output doesn’t meet standards

If results are acceptable no further action is required

Unacceptable results call for correction action

Phases of Quality Assurance:

Inspection: An appraisal activity that compares goods or services to a standard

Inspection issues:

1. How much to inspect and how often

2. At what points in the process to inspect

3. Whether to inspect in a centralized or on-site location

4. Whether to inspect variables or attributes

How Much to Inspect?

Typical Inspection Points:

Purchased parts and raw materials

Finished products

Before a costly operation

Before an irreversible process

Before a covering process

Effects on cost and level of disruption are a major issue in selecting centralized vs. on-site inspection

Centralized

Specialized tests that may best be completed in a lab

More specialized testing equipment

More favorable testing environment

On-site

Quicker decisions are rendered

Avoid introduction of extraneous factors

Quality at source

Statistical Process Control (SPC)

Quality control seeks

Quality of Conformance

A product or service conforms to specifications

A tool used to help in this process - SPC

Statistical evaluation of the output of a process

Helps us to decide if a process is “in control” or if corrective action is needed

Process Variability

Two basic questions concerning variability:

Issue of process control

Are the variations random? If nonrandom variation is present, the process is said to be unstable.

Issue of process capability

Given a stable process, is the inherent variability of the process within a range that conforms to performance criteria?

Variation

Random(common cause) variation:

Natural variation in the output of a process, created by countless minor factors

Assignable(special cause) variation:

A variation whose cause can be identified.

A nonrandom variation

Sampling and Sampling Distribution

o SPC involves periodically taking samples of process output and computing sample statistics:

Sample means

The number of occurrences of some outcome

o Sample statistics are used to judge the randomness of process variation

o Sampling Distribution

A theoretical distribution that describes the random variability of sample statistics

The normal distribution is commonly used for this purpose

o Central Limit Theorem

The distribution of sample averages tends to be normal regardless of the shape of the process distribution

Control Process

o Sampling and corrective action are only a part of the control process

o Steps required for effective control:

Define: What is to be controlled?

Measure: How will measurement be accomplished?

Compare: There must be a standard of comparison

Evaluate: Establish a definition of out of control

Correct: Uncover the cause of nonrandom variability and fix it

Monitor results: Verify that the problem has been eliminated

Control Charts: The voice of the Process

o Control Chart

A time ordered plot of representative sample statistics obtained from an ongoing process (e.g. sample means), used to distinguish between random and nonrandom variability

o Control limits

The dividing lines between random and nonrandom deviations from the mean of the distribution

Upper and lower control limits define the range of acceptable variation

Errors

Type I error

Concluding a process is not in control when it actually is.

The probability of rejecting the null hypothesis when the null hypothesis is true.

Manufacturer’s Risk

Type II error

Concluding a process is in control when it is not.

The probability of failing to reject the null hypothesis when the null hypothesis is false.

Consumer’s Risk

Control Charts for Variables

Variables generate data that are measured

Mean control charts Used to monitor the central tendency of a process.

“x- bar” charts Range control charts

Used to monitor the process dispersionR charts

Using Mean and Range Charts

o To determine initial control limits:

Obtain 20 to 25 samples

Compute appropriate sample statistics

Establish preliminary control limits

Determine if any points fall outside of the control limits

If you find no out-of-control signals, assume the process is in control

If you find an out-of-control signal, search for and correct the assignable cause of variation

Resume the process and collect another set of observations on which to base control limits

Plot the data on the control chart and check for out-of-control signals

Example of Using x-bar and R-charts:

The management of West Allis Industries is concerned about the production of a special metal screw used by several of the company’s largest customers. The diameter of the screw is critical

to the customers. Data from five samples (number of groups) appear in the accompanying table. The sample size (group size) is 4. Is the process in statistical control?

SOLUTION

Step 1: For simplicity, we use only 5 samples. In practice, more than 20 samples would be desirable. The data are shown in the following table.

Step 2: Compute the range for each sample by subtracting the lowest value from the highest value. For example, in sample 1 the range is 0.5027 – 0.5009 = 0.0018 in. Similarly, the ranges for samples 2, 3, 4, and 5 are 0.0021, 0.0017, 0.0026, and 0.0022 in., respectively. As shown in the table, R = 0.0021.

Step 3: To construct the R-chart, select the appropriate constants from Table 5.1 for a sample size of 4. The control limits are

.00479

0

Step 4: Plot the ranges on the R-chart, as shown in Figure 5.10. None of the sample ranges falls outside the control limits so the process variability is in statistical control. If any of the sample ranges fall outside of the limits, or an unusual pattern appears, we would search for the causes of the excessive variability, correct them, and repeat step 1.

Step 5: Compute the mean for each sample. For example, the mean for sample 1 is

Similarly, the means of samples 2, 3, 4, and 5 are 0.5027, 0.5026, 0.5020, and 0.5045 in., respectively. As shown in the table, x-double Bar = 0.5027.

Control Charts for Attributes

Attributes generate data that are counted.

o p-Chart

Control chart used to monitor the proportion of defectives in a process

o c-Chart

Control chart used to monitor the number of defects per unit

Using a p-chart

o When observations can be placed into two categories.

Good or bad

Pass or fail

Operate or don’t operate

o When the data consists of multiple samples of several observations each

Using a p-chart Example:

Hometown Bank is concerned about the number of wrong customer account numbers recorded

Each week a random sample of 2,500 deposits is taken and the number of incorrect account numbers is recorded

The results for the past 12 weeks are shown in the following table

Is the booking process out of statistical control?

Use three-sigma control limits, which will provide a Type I error of 0.26 percent.

Sample Number

Wrong Account Numbers

Sample Number

Wrong Account Numbers

1 15 7 24

2 12 8 7

3 19 9 10

4 2 10 17

5 19 11 15

6 4 12 3

Total 147

Solution:

Using a c-chart: Use only when the number of occurrences per unit of measure can be counted; non-occurrences cannot be counted.

o Scratches, chips, dents, or errors per item

o Cracks or faults per unit of distance

o Breaks or Tears per unit of area

o Bacteria or pollutants per unit of volume

o Calls, complaints, failures per unit of time

Using a c-Chart Example:

The Woodland Paper Company produces paper for the newspaper industry. As a final step in the process, the paper passes through a machine that measures various product quality characteristics. When the paper production process is in control, it averages 20 defects per roll.

o Set up a control chart for the number of defects per roll. For this example, use two-sigma control limits.

o Five rolls had the following number of defects: 16, 21, 17, 22, and 24, respectively. The sixth roll, using pulp from a different supplier, had 5 defects. Is the paper production process in control?

Managerial Considerations

At which points in the process to use control charts

What size samples to take

What type of control chart to use

o Variables

o Attributes

Run Tests

Even if a process appears to be in control, the data may still not reflect a random process

Analysts often supplement control charts with a run test

o Run test

A test for patterns in a sequence

o Run

Sequence of observations with a certain characteristic

Process Capability

Once a process has been determined to be stable, it is necessary to determine if the process is capable of producing output that is within the acceptable range

o Tolerances or specifications

Range of acceptable values established by customer requirements or engineering design

o Process variability

Natural or inherent variability in a process

o Process capability

The inherent variability of process output (process width) relative to the variation allowed by the design specification (specification width)

Cp: Process Capability Ratio

UTL-LTL/6σ

Where:

UTL = upper tolerance limit

LTL = lower tolerance limit

Cpk : Process Capability Index

Used when a process is not centered at its target, or nominal, value

Cpk = min{Cpu,Cpl}

= min{UTL-x/3σ, x-LTL/3σ

Improving Process Capability

Simplify

Standardize

Mistake-proof

Upgrade equipment

Automate

Operations Strategy: Quality is a primary consideration for nearly all customerso Achieving and maintaining quality standards is of strategic importance to all

business organizations Product and service design Increase capability in order to move from extensive use of control charts

and inspection to achieve desired quality outcomes